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Now let us assume that the ray has come from A to C along AK, KC; the point of refraction K being nearer to A than the point B is; and let CN be the perpendicular upon BC, KN parallel to BC: BM perpendicular upon KN, and KL upon BA.
A tall figure joined William, awkwardiy. "Hello, Evan!" "How is he, Bm?" "He's awake today." "That's good. Anything I can do?" "No, I guess not. An he needs is somethin' to eat." "I jest brought a chicken up, an' some jell an' things the women sent. I'll stay with him till twelve, then Folsom will come in."
Through the line BM, and through the points O and A, let there be drawn planes parallel to one another, which, in cutting the spheroid make the ellipses LBD, POP, QAQ; which will all be similar and similarly disposed, and will have their centres K, N, R, in one and the same diameter of the spheroid, which will also be the diameter of the ellipse made by the section of the plane that passes through the centre of the spheroid, and which cuts the planes of the three said Ellipses at right angles: for all this is manifest by proposition 15 of the book of Conoids and Spheroids of Archimedes.
The first law is that Natives belonging to class A may only intermarry with class B, and natives belonging to C may only intermarry with class D. The progeny of a man and woman of intermarrying classes is of a different class from either father or mother. Let Am represent a male of class A. Let Af represent a female of class A, and similarly Bm, Bf, &c.
All the progeny of classes A and B are brothers and sisters; similarly C and D. Thus taking Dp2 to represent the progeny of an Ap and a Bp Af + Bm Ap + Bp Dp Dp2 For this reason there is no absurdity in a small boy pointing out a very aged woman as his sister. A man may have as many wives as he can get, so long as these laws are adhered to.
And it is manifest that the demonstration would be the same if, besides the points O, A, there had been others in which the spheroid had been touched by planes parallel to the straight line BM. Which serve for Refraction and for Reflexion
Further, the two latter planes, which are drawn through the points O and A, will also, by cutting the planes which touch the spheroid in these same points, generate straight lines, as OH and AS, which will, as is easy to see, be parallel to BM; and all three, BM, OH, AS, will touch the Ellipses LBD, POP, QAQ in these points, B, O, A; since they are in the planes of these ellipses, and at the same time in the planes which touch the spheroid.
If now from these points B, O, A, there are drawn the straight lines BK, ON, AR, through the centres of the same ellipses, and if through these centres there are drawn also the diameters LD, PP, QQ, parallel to the tangents BM, OH, AS; these will be conjugate to the aforesaid BK, ON, AR. And because the three ellipses are similar and similarly disposed, and have their diameters LD, PP, QQ parallel, it is certain that their conjugate diameters BK, ON, AR, will also be parallel.
But the mother never quite despaired, and she had a feeling that somehow the little clog would help her in her search: on its wooden sole, as well as on that of the lost one, she had scratched two letters BM. "So the time went on and on. It was seven long years after she had lost her child that the mother heard of a situation in a place called Wensdale, and went there to live.
Thinking thus, and rubbing it meanwhile, she noticed for the first time that there were two letters faintly scratched on the wooden sole, "BM." Who was BM? "Perhaps that's my name," she thought; "but I don't want to know it if it is. I'd rather be Mary Vallance." And then the dark faces of Perrin and Seraminta came before her and she frowned. How hateful it was to belong to them!
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